Independent Component Analysis of Real Data

Abstract

Independent component analysis (ICA) is a statistical method used to discover hidden factors (sources or features) from a set of measurements or observed data such that the sources are maximally independent. The ICA algorithms are able to separate the sources according to the distribution of the data. The original Infomax algorithm for blind separation is better suited to estimation of super-Gaussian sources. FastICA can separate the sources having non-Gaussian distributions. Real data (e.g. functional magnetic resonance imaging (fMRI) data and speech signal obtained at cocktail party problem) is having Gaussian and non-Gaussian distributions. So existing ICA algorithms such as the Infomax, FastICA can not separate the independent components from the real data. For proper separation of independent components we have tried with different ICA algorithms. Recently developed Combi ICA can separate the independent components from real data faithfully. Because the Combi ICA can separate the sources having non-Gaussian and Gaussian distributions. In this paper, we find the independent components by a number of ICA algorithms from which Efficient FastICA and Combi ICA are found to be good because the accuracy in terms of the variance of the Gain matrix (Amari Performance Index) is more as compared to others. In our work we 1) used the kurtosis and negentropy to know the distribution of data 2) review the analysis methods for finding independent components from real data (specially fMRI data), 3) comparison of different ICA algorithms. The purpose of this work is to have an idea about the problems, challenges and methods about analysis of independent components from real data.